Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 36
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 150242670864249019283283734952440734379/201055517588041462530306433067873447*t^39 + 50543970073899062469657084528036329598177/201055517588041462530306433067873447*t^37 - 10149808554700615983939299074490427271306035/201055517588041462530306433067873447*t^35 + 80016575766228661280836932349507530018219330/11826795152237733090018025474580791*t^33 - 7581965382429899272565221568903557331526406380/11826795152237733090018025474580791*t^31 + 525067773804616599714198858449227699470793659540/11826795152237733090018025474580791*t^29 - 27100617512043387767226016865706587381092712535420/11826795152237733090018025474580791*t^27 + 1053921124392549316967178772861330882105063046383050/11826795152237733090018025474580791*t^25 - 31027027018141170938770646455801175683572100559630250/11826795152237733090018025474580791*t^23 + 691287629681260503947801427208367968991969654828028750/11826795152237733090018025474580791*t^21 - 11601895835178407084448811450545325496844712476013610250/11826795152237733090018025474580791*t^19 + 145347344848122940394338782516921530414816644729228932000/11826795152237733090018025474580791*t^17 - 1340359978762624543409995757154053690187707482347665437500/11826795152237733090018025474580791*t^15 + 8917382655163817562554658376881317492861800119546879502500/11826795152237733090018025474580791*t^13 - 41590768603362642077773390359228255545927497479779868307500/11826795152237733090018025474580791*t^11 + 130402165991881882485947088812746057603452820701762376314375/11826795152237733090018025474580791*t^9 - 257717460101339943447813946260953656259052327844145734861875/11826795152237733090018025474580791*t^7 + 288716657539005346582007637954959922577755326291048840915625/11826795152237733090018025474580791*t^5 - 150688904957231736995270509700047923324982247789190076396875/11826795152237733090018025474580791*t^3 + 23166880717692220669694889110250473225370569685005810793750/11826795152237733090018025474580791*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (8.0996726796116371908 + 7.331415463126617428e-689j)  +/-  (1.78e-245, 1.78e-245j)
| (11.290071640558007609 - 1.0178131074333167575e-692j)  +/-  (5.57e-248, 5.57e-248j)
| (-11.290071640558007609 + 1.4463433815171700477e-689j)  +/-  (6.57e-248, 6.57e-248j)
| (-5.70088869884274181 - 3.8279705599030412038e-701j)  +/-  (9.37e-246, 9.37e-246j)
| (-8.0996726796116371908 + 7.6137635849692095163e-719j)  +/-  (1.5e-245, 1.5e-245j)
| (-9.5017383588396716198 - 1.4187707374051603482e-729j)  +/-  (3.09e-246, 3.09e-246j)
| (-3.0323961210426638904 - 1.4047844012751075866e-739j)  +/-  (6.48e-248, 6.48e-248j)
| (8.7739119570397350598 - 1.5036842379773849876e-736j)  +/-  (8.68e-246, 8.68e-246j)
| (-2.4494897427831780982 - 2.2548343336778232499e-739j)  +/-  (3.97e-248, 3.97e-248j)
| (-10.313734641430242516 + 1.2553123029137762131e-737j)  +/-  (6.55e-247, 6.55e-247j)
| (9.5017383588396716198 + 3.9213883394122206346e-742j)  +/-  (2.95e-246, 2.95e-246j)
| (-8.7739119570397350598 + 6.0971690054815316346e-744j)  +/-  (8.85e-246, 8.85e-246j)
| (10.313734641430242516 + 6.1735058177130517571e-749j)  +/-  (6.56e-247, 6.56e-247j)
| (-2.0043224503564302899 - 3.6983215303848353012e-752j)  +/-  (1.1e-249, 1.1e-249j)
| (6.8551936516883123424 + 1.2083157133294888954e-747j)  +/-  (1.89e-245, 1.89e-245j)
| (6.2692138179245508769 + 3.5940974641687898551e-753j)  +/-  (1.55e-245, 1.55e-245j)
| (3.5486167650462948215 - 4.4904671750919537334e-761j)  +/-  (1.83e-247, 1.83e-247j)
| (-1 - 4.2868181798745006017e-766j)  +/-  (2.52e-252, 2.52e-252j)
| (-4.0725434408451943524 + 6.1492944965556196455e-761j)  +/-  (5.75e-247, 5.75e-247j)
| (-6.8551936516883123424 - 1.3758608659485206606e-773j)  +/-  (1.99e-245, 1.99e-245j)
| (2.4494897427831780982 + 8.7241929711406057838e-797j)  +/-  (3.75e-248, 3.75e-248j)
| (2.5443329143988662185 + 1.4168828435521219207e-795j)  +/-  (5.41e-248, 5.41e-248j)
| (-6.2692138179245508769 + 1.2222965874663675872e-800j)  +/-  (1.48e-245, 1.48e-245j)
| (-2.5443329143988662185 + 1.250954044120133564e-813j)  +/-  (5.63e-248, 5.63e-248j)
| (-3.5486167650462948215 + 1.4035983075721064511e-813j)  +/-  (1.84e-247, 1.84e-247j)
| (1 + 6.0086019515359320017e-818j)  +/-  (3.32e-252, 3.32e-252j)
| (4.0725434408451943524 + 9.7162518974487882602e-811j)  +/-  (6.09e-247, 6.09e-247j)
| (-7.4632577760565035479 - 1.5225720304771157715e-817j)  +/-  (1.97e-245, 1.97e-245j)
| (7.4632577760565035479 - 3.9838918714994735455e-822j)  +/-  (1.99e-245, 1.99e-245j)
| (5.70088869884274181 + 1.6338743446921765562e-824j)  +/-  (8.75e-246, 8.75e-246j)
| (-5.1469306854594306625 - 1.707037797500929705e-825j)  +/-  (4.1e-246, 4.1e-246j)
| (1.5016390046673233736 - 1.1694412182014932977e-835j)  +/-  (5.16e-251, 5.16e-251j)
| (3.0323961210426638904 - 3.2252419966409651284e-832j)  +/-  (7.2e-248, 7.2e-248j)
| (2.0043224503564302899 + 2.2583796828886719518e-834j)  +/-  (1.36e-249, 1.36e-249j)
| (6.0959848359493612511e-852 + 3.2525637262300956716e-852j)  +/-  (2.83e-850, 2.83e-850j)
| (-4.6048106388153598497 - 6.3033617797754240012e-831j)  +/-  (1.57e-246, 1.57e-246j)
| (5.1469306854594306625 + 4.9733766101414522972e-832j)  +/-  (4.35e-246, 4.35e-246j)
| (0.49965061297185557927 + 1.2767334277961074606e-841j)  +/-  (1.29e-253, 1.29e-253j)
| (4.6048106388153598497 - 1.1781806274182413336e-837j)  +/-  (1.74e-246, 1.74e-246j)
| (-1.5016390046673233736 - 9.9216396411219501708e-843j)  +/-  (5.15e-251, 5.15e-251j)
| (-0.49965061297185557927 + 3.9887790403371045903e-846j)  +/-  (1.29e-253, 1.29e-253j)
-------------------------------------------------
The weights are:
| (1.4797633399774673061e-15 - 4.6890593653189442397e-703j)  +/-  (1.86e-82, 7.12e-205j)
| (9.4051827539035886834e-29 + 4.2021085534880290314e-711j)  +/-  (2.73e-88, 1.05e-210j)
| (9.4051827539035886834e-29 - 6.9140925692395234844e-712j)  +/-  (2.44e-89, 9.33e-212j)
| (1.9602004213180781964e-08 - 6.4527934323172420328e-701j)  +/-  (1.76e-78, 6.76e-201j)
| (1.4797633399774673061e-15 - 6.6970324665636978988e-705j)  +/-  (3.03e-84, 1.16e-206j)
| (7.5609921482026178512e-21 - 9.8466553360363055939e-708j)  +/-  (6.09e-87, 2.33e-209j)
| (0.0020571335407555590894 + 2.2236686793209390817e-697j)  +/-  (6.65e-71, 2.55e-193j)
| (5.3481089447008417754e-18 - 8.1199538180141545161e-705j)  +/-  (4.31e-87, 1.65e-209j)
| (0.0031469524477469398666 + 3.4394001738291729057e-696j)  +/-  (9.33e-69, 3.57e-191j)
| (2.7733986397374461971e-24 + 1.513330478240316164e-709j)  +/-  (1.3e-88, 4.97e-211j)
| (7.5609921482026178512e-21 + 1.2361418259227602862e-706j)  +/-  (9.51e-89, 3.64e-211j)
| (5.3481089447008417754e-18 + 3.2445909647336807734e-706j)  +/-  (2.09e-86, 7.99e-209j)
| (2.7733986397374461971e-24 - 1.2585747236991600075e-708j)  +/-  (2.65e-90, 1.01e-212j)
| (0.026869556229618940853 - 1.2806125474521596982e-696j)  +/-  (3.62e-70, 1.39e-192j)
| (1.4849978978786392596e-11 - 1.2710180852203380947e-701j)  +/-  (8.04e-86, 3.08e-208j)
| (6.7170989641437272741e-10 + 7.159075037597200074e-701j)  +/-  (3.72e-85, 1.42e-207j)
| (0.00038241927235135300689 - 1.1146106053694427577e-697j)  +/-  (3.06e-80, 1.17e-202j)
| (0.12120705627942982897 - 1.2496686591134218845e-696j)  +/-  (1.02e-72, 3.92e-195j)
| (5.2714743223789138855e-05 + 9.5670467372729190153e-699j)  +/-  (1.55e-80, 5.94e-203j)
| (1.4849978978786392596e-11 - 1.0576856846879108215e-702j)  +/-  (4.11e-86, 1.57e-208j)
| (0.0031469524477469398666 + 6.4215255110132370033e-696j)  +/-  (1.12e-77, 4.29e-200j)
| (0.005704974419221083748 - 5.5619320821099198029e-696j)  +/-  (5.27e-78, 2.02e-200j)
| (6.7170989641437272741e-10 + 9.1199748834619501575e-702j)  +/-  (1.04e-85, 3.99e-208j)
| (0.005704974419221083748 - 2.9028940005242854755e-696j)  +/-  (3.64e-77, 1.39e-199j)
| (0.00038241927235135300689 - 4.354849367764078957e-698j)  +/-  (1.27e-80, 4.85e-203j)
| (0.12120705627942982897 - 1.6017042777222316339e-696j)  +/-  (1.43e-77, 5.48e-200j)
| (5.2714743223789138855e-05 + 2.8916920653709682656e-698j)  +/-  (1.63e-84, 6.23e-207j)
| (1.9899708086432890804e-13 + 9.6989856158487584685e-704j)  +/-  (5.92e-88, 2.27e-210j)
| (1.9899708086432890804e-13 + 2.3717970885123359935e-702j)  +/-  (1.21e-89, 4.64e-212j)
| (1.9602004213180781964e-08 - 3.7123888684106034912e-700j)  +/-  (9.51e-88, 3.64e-210j)
| (3.8636914469841875677e-07 + 3.8654262907916848731e-700j)  +/-  (1.09e-85, 4.16e-208j)
| (0.064907677061683366805 + 1.6684239870456862547e-696j)  +/-  (3.54e-81, 1.36e-203j)
| (0.0020571335407555590894 + 4.8850767990866102743e-697j)  +/-  (1.31e-83, 5.02e-206j)
| (0.026869556229618940853 - 2.1228154678132301359e-696j)  +/-  (3.66e-82, 1.4e-204j)
| (0.19928446674898542392 - 1.5069940891304373364e-696j)  +/-  (5.17e-82, 1.98e-204j)
| (5.325417581633320121e-06 - 2.0209781535170863104e-699j)  +/-  (9.88e-86, 3.78e-208j)
| (3.8636914469841875677e-07 + 1.7341094570254287483e-699j)  +/-  (8.68e-88, 3.32e-210j)
| (0.17602355055598552405 + 1.5734176777200894805e-696j)  +/-  (8.76e-84, 3.14e-206j)
| (5.325417581633320121e-06 - 7.3466383146764538288e-699j)  +/-  (4.71e-87, 1.81e-209j)
| (0.064907677061683366805 + 1.1465430459676461481e-696j)  +/-  (2.01e-84, 8.3e-207j)
| (0.17602355055598552405 + 1.3905755701160875891e-696j)  +/-  (4.22e-84, 1.37e-206j)
